The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1 2X 4X  1  0  1  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1 2X  1  1  1  1  X  1 2X  1  1 3X 4X 4X  1  1
 0  1  0  0 3X 4X 3X+1 4X+1  1 3X+2  4 3X+3  1  1 X+4  1  2 4X+3 X+2  1  2 2X+1 3X 2X+4  3 4X+2 4X+4 2X+2  0 4X+2 X+3  3 2X+1 2X+1 2X+4 3X+4 4X+4 X+3 3X+1 4X  X X+4  1 2X 3X+3  X 3X+2  1 4X+2  1 2X+2 3X  1  1 3X 3X+1  X
 0  0  1  0 3X+1 3X+2 3X+3  1 4X+2 X+1  2 2X+3 3X+2 2X+3 X+3  1 3X X+2 3X+3 2X+4 4X+2 3X 4X 2X+1  X  1 4X 4X+2 4X+1 3X+2 3X+4  2 2X 2X+4 2X+4 2X+1 4X+1  3  X  1 2X+4 4X 2X+1 3X+4  1 X+3  X 4X+4  4 2X  X 2X+4 4X+4 2X+2  1 3X+2 4X
 0  0  0  1 3X+3 3X+2 4X+3 3X+1  X 4X+2 X+1 2X X+4  2 4X+4 X+3 2X+4 X+4 X+2 2X 3X 2X+2 3X+1 3X 2X X+3 X+2 X+4 3X+4 2X+1 2X+1 4X+2 2X+4 4X+4 3X+1  2 4X+3 2X+4 2X+1 4X+1 3X+2 X+4 3X+2  3 2X+1 X+1 4X+3  2 3X+4 3X+4 4X X+1 4X+4 3X 4X+4 4X+3 2X+2

generates a code of length 57 over Z5[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+500x^208+520x^209+956x^210+1700x^211+2480x^212+3600x^213+3100x^214+4924x^215+5520x^216+7060x^217+9620x^218+7980x^219+10248x^220+10620x^221+12240x^222+17800x^223+15480x^224+16324x^225+17520x^226+18180x^227+28080x^228+22380x^229+22284x^230+21220x^231+19120x^232+26760x^233+17760x^234+16736x^235+13220x^236+11080x^237+10340x^238+5280x^239+4088x^240+2700x^241+2340x^242+800x^243+24x^245+16x^250+8x^255+4x^260+4x^265+4x^270+4x^280

The gray image is a linear code over GF(5) with n=285, k=8 and d=208.
This code was found by Heurico 1.16 in 198 seconds.